Question

A taxable bond with a coupon rate of 5.00% has a market price of 98.14% of par. The bond matures in 12.00 years ans pays semi-annually. Assume an investor has a 36.00% marginal tax rate. The investor would prefer otherwise identical tax-exempt bond if it's yield to maturity was more than _____%

SHOW WORK FOR FINANCIAL CALCULATOR PLEASE

Answer 1

The Yield to maturity (YTM) of the Bond

· The Yield to maturity (YTM) of the Bond is the discount rate at which the Bond’s price equals to the present value of the coupon payments plus the present value of the Face Value/Par Value

· The Yield to maturity of (YTM) of the Bond is the estimated annual rate of return expected by the bondholders for the bond assuming that the they hold the Bonds until it’s maturity period/date.

· The Yield to maturity of (YTM) of the Bond is calculated using financial calculator as follows (Normally, the YTM is calculated either using EXCEL Functions or by using Financial Calculator)

Variables	Financial Calculator Keys	Figure
Par Value/Face Value of the Bond [$1,000]	FV	1,000
Coupon Amount [$1,000 x 5.00% x ½]	PMT	25
Market Interest Rate or Yield to maturity on the Bond	1/Y	?
Maturity Period/Time to Maturity [12 Years x 2]	N	24
Bond Price/Current Market Price of the Bond [-$1,000 x 98.14%]	PV	-981.40

We need to set the above figures into the financial calculator to find out the Yield to Maturity of the Bond. After entering the above keys in the financial calculator, we get the semi-annual yield to maturity on the bond (1/Y) = 2.605%.

The semi-annual Yield to maturity = 2.605%.

Therefore, the annual Yield to Maturity of the Bond = 5.21% [2.605% x 2]

The after-tax Yield to maturity (YTM) of the Bond

The firm’s after-tax cost of debt on the Bond is the after-tax Yield to maturity (YTM)

The After-tax cost of debt = Annual Yield to maturity on the bond x (1 – Tax Rate)

= 5.21% x (1 – 0.36)

= 5.21% x 0.64

= 3.33%

“Hence, the investor will prefer otherwise identical tax-exempt bond if it's yield to maturity was more than 3.33%”